Group Spreading: A Protocol for Provably Secure Distributed Name Service

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Group Spreading A Protocol for Provably Secure
Distributed Name Service

• Christian Scheideler
• Dept. of Computer Science
• Johns Hopkins University
• Joint work with Baruch Awerbuch

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Name Service

• Peer entity with a unique identity, i.e.
  identified by (Name(p), IP(p))
• Goal provide name service, i.e. each execution
  of Lookup(name) returns IP(p) of the peer p with
  Name(p)name, or NULL if there is no such peer

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Name Service

• Static set of peers.
• Easiest solution every peers knows every other
  peer.
• Problem not scalable!
• Better solution peers organize in a searchable
  overlay network of low degree.

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Chord

• Stoica, Morris, Karger, Kaashoek, and
  Balakrishnan 01
• Idea organize peers in cycle according to
• hash function hNames 0,1).

0.28
0.43
0.58
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Hypercubic Shortcuts
1 0
1/2
1/4
fingers
1/8
1/16
x
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Hypercubic Pointer Structure
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Lookup Operation

• Lookup(name) log n number of hops

Pure Chord cannot handle adversarial peers!!
Can also handle dynamic set of peers.
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Distributed Name Service

• Dynamic set of peers, some adversarial.
• Operations
• Join(p) peer p wants to join the system
• Leave(p) peer p wants to leave the system
• Lookup(name) returns IP(p) of the peer p with
  Name(p)name, or NULL if there is no such peer
• Goal Provide provably survivable distributed
  name service

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Prerequisites

• Certification authority
• certifies (Name,IP) pairs so that collisions are
  avoided
• prevents adversarial peers from taking over
  identity of honest peers
• cannot prevent adversarial peers from registering
  (potentially many) own pairs

Fighting at this front is fighting the wrong
battle!
Allow adversary to have infinitely many
identities, but resources finite!
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Correctness

• Once Join(p) or Leave(p) terminates in p, it is
  called completed.
• p is called a member once Join(p) has completed.
• p ceases to be a member once it initiates
  Leave(p).
• Lookup(name) request executed correctly
• If an honest peer p with Name(p) name is
  currently a member of the system, returns IP(p).
• Otherwise, if such a peer has never been in the
  system or completed Leave(p) , returns NULL.
• Otherwise, returns IP(p) or NULL.

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Efficiency

• Time unit max time a message needs to travel
  from one honest peer to another
• An overlay network operation is called
• work-efficient if it is completed using a comm
  volume of at most polylog(n) bits
• time-efficient if it is completed in at most
  polylog(n) time units
• Overlay network maintainance should only need
  polylog(n) bits of comm per time unit per peer

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Peer-to-Peer Name Service

• Problem adversarial peers a priori
  indistinguishable from honest peers

• Idea randomly distribute peers in overlay
  networkCAN,Chord,Pastry,
• Strategy use pseudo-random hash function hNames
  0,1)

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Peer-to-Peer Name Service

• Place peer p at h(name(p)) in 0,1)
• randomly distributes honest peers
• may not randomly distribute adversarial peers

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Peer-to-Peer Name Service
Problem adversarial peers can isolate honest
peers

• Chord connect to
• direct neighbors
• closest successor of h(Name(p))1/2

i
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Peer-to-Peer Name Service

• Alternative
• Assign each peer p to a random ID(p) in 0,1)

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Peer-to-Peer Name Service

• New attempt
• Assign each peer p to a random ID(p)
• Limit lifetime of a peer

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Peer-to-Peer Name Service

• So good approach
• Assign random IDs
• Enforce limited lifetime
• But
• How to interconnect the peers?
• How to generate random IDs?
• How to enforce limited lifetime?
• How to implement operations?

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Peer-to-Peer Name Service

• How to interconnect the peers?
• Region approach each peer has several nodes,
  each node v maintains rvlog n - loglog n Q(1)

0
1
Region interval of size 1/2r starting at an
integral multiple of 1/2r. 1/2rv Q(log n / n)
/- 1/2
-1/4
1/4
-1/8
1/8
x
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Peer-to-Peer Name Service

• How to generate random IDs?
• Group approach each peer maintains Q(log n)
  nodes, ID of new node generated by region

a)
b)
c)
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Peer-to-Peer Name Service

• How to enforce limited lifetime?
• Lifetime approach
• Join operation implemented s.t. it either
  terminates in Q(log n) steps or does not succeed
• Honest nodes take median of age views of a node
  reported by nodes in region
• Honest nodes cut connections to nodes that are
  more than LQ(log n) steps old

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Peer-to-Peer Name Service

• How to implement operations?
• Join(p) p contacts a peer q in the system, q
  includes Q(log n) nodes for p into the system,
  from there p inserts entry (Name(p),IP(p)) into
  relevant region and takes over maintenance of its
  nodes
• Leave(p) p deletes entry (Name(p),IP(p)) and
  leaves the system
• Lookup(name) region routing, majority decision

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Assumptions

• adversary e/log n - bounded
• join/leave rate of peers is O(1/log2 N)
• honest peers have infinite bandwidth (no DOS)
• assumptions about messages
• A peer is honest if
• it is not under the control of the adversary at
  any time,
• it is reliable, and
• it contacted an honest peer in order to join the
  network.

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Related Work

• Classical distributed computing Byzantine
  agreement, two-phase commit, linear overhead
• Proactive security uses coding to protect data
  in dynamic environment, linear overhead
• Fixed-topology networks only fail-stop faults,
  no Byzantine behavior
• Hash-based P2P networks hinge on assumption that
  IDs are random
• Random or unpredictable placement (Freenet,
  Gnutella) hard to attack, but hard to find data

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Related Work

• Sit and Morris 2001 investigate various
  attacks and defenses including routing attacks,
  storage and retrieval attacks, DoS, and
  join/leave attacks
• Castro, 2001 replication algorithm tolerating
  Byzantine faults as long as 1/3 fraction of
  replicas faulty
• Douceur, 2002 Sybil attacks (adversaries forge
  multiple identities)
• Castro, Druschel, Ganesh, 2002 strategies for
  secure nodeID assignment, routing table
  maintenance, and message forwarding
• BUT no provably robust overlay construction

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Comparison

• Group Spreading e/log N-bounded adversary
• Enforced Spreading e-bounded adversary

N
Trust-but-Verify
work
overhead
Group Spreading
polylog(N)
Enforced Spreading
0
fraction of adv nodes
e/log N
e
1/2
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Conclusions

• It is possible to come up with provably robust
  overlay network constructions!
• Analysis hard
• Model still unrealistic, but Rome was also not
  built in one day ?
• Questions????

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STOC 2005
When May 22-24, 2005 Where Baltimore, MD,
USA Submission deadline Nov 4, 559 pm EST Web
Site www.cs.jhu.edu/stoc05